{"paper":{"title":"Mutual information decay for factors of IID","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Bal\\'azs Gerencs\\'er, Viktor Harangi","submitted_at":"2017-03-13T13:43:52Z","abstract_excerpt":"This paper is concerned with factor of i.i.d. processes on the $d$-regular tree for $d \\geq 3$. We study the mutual information of the values on two given vertices. If the vertices are neighbors (i.e., their distance is $1$), then a known inequality between the entropy of a vertex and the entropy of an edge provides an upper bound for the (normalized) mutual information. In this paper we obtain upper bounds for vertices at an arbitrary distance $k$, of order $(d-1)^{-k/2}$. Although these bounds are sharp, we also show that an interesting phenomenon occurs here: for any fixed process the rate "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04387","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}